## Magnets and Their Fields!

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z4lis
Posts: 767
Joined: Mon Mar 03, 2008 10:59 pm UTC

### Magnets and Their Fields!

Okay. So I'm working on a problem, and I'll deliver here in a simplified form that'll help me dig up the answer without flat out giving it to me. Say I've got this uniform magnetic field and in that field I stick an iron bar. Can I just add up the uniform field and the magnetized bar's fields separately to find the resulting field, or does it do something more complicated than that? I have a hunch that it's the latter, as I've seen illustrations of ferromagnetic spheres in uniform fields that bend the uniform field around in ways I can't explain by just "adding up" the components. Any help here, XKCD? An illuminating page or explanation on how to actually use Maxwell's equations to solve problems would be more appreciated than anything.
What they (mathematicians) define as interesting depends on their particular field of study; mathematical anaylsts find pain and extreme confusion interesting, whereas geometers are interested in beauty.

danpilon54
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### Re: Magnets and Their Fields!

edit: sorry I thought I knew but I think I convinced myself I didn't
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Cynwulf
Posts: 208
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Location: California

### Re: Magnets and Their Fields!

I'm not the physicist in the family, and I really really really don't want to do vector calculus. It has been years, and I'm still sore >_<

However, I recall that magnetic fields are vectors. So you have a magnitude and a direction. Let's say your uniform magnetic field is one dimensional (positive y direction) and you stick your dipole magnet in the field. Your dipole magnet's field, normally a kind of nice circular shape, would get stretched in the positive y direction due to the uniform field, making the dipole magnet's field into an stretchy ellipsoid. Assuming both fields are roughly the same magnitude. I think. >>;

Disclaimer: I'm probably wrong.

On a related note: where the hell are the physicists? C'mon people! Don't let the stupid engineer mess up Maxwell's equations!
L'homme est libre au moment qu'il veut l'être. | Man is free at the instant he wants to be.
- Voltaire

Tass
Posts: 1909
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Location: Niels Bohr Institute, Copenhagen.

### Re: Magnets and Their Fields!

Only thing to worry about is if the bars own field changes it magnetization so that the magnetization is not uniform. If the bar is long and thin and aligned with the field, then just add the field from the pseudo monopoles at its ends to the uniform field.

z4lis
Posts: 767
Joined: Mon Mar 03, 2008 10:59 pm UTC

### Re: Magnets and Their Fields!

Come to think of it, the material probably would change its own magnetization. It seems like actually finding the field in that situation would involve solving some PDE's, which I'm by no means equipped to do at the moment....
What they (mathematicians) define as interesting depends on their particular field of study; mathematical anaylsts find pain and extreme confusion interesting, whereas geometers are interested in beauty.

cypherspace
Posts: 2733
Joined: Thu Jan 10, 2008 9:48 pm UTC
Location: Londonia

### Re: Magnets and Their Fields!

Okay. So I'm working on a problem, and I'll deliver here in a simplified form that'll help me dig up the answer without flat out giving it to me. Say I've got this uniform magnetic field and in that field I stick an iron bar. Can I just add up the uniform field and the magnetized bar's fields separately to find the resulting field, or does it do something more complicated than that?
It depends where you're measuring the field. Within the bar, you should have a single field value defined by the strength of the uniform magnetic field + the field created by the net magnetisation of the bar (which should be uniform field strength * relative permeability), but outside the bar the field will change non-linearly. In practice an iron bar is not uniform and the field within the bar will also be non-uniform.
"It was like five in the morning and he said he'd show me his hamster"

Matterwave1
Posts: 226
Joined: Wed Aug 20, 2008 7:01 pm UTC

### Re: Magnets and Their Fields!

As far as I know, magnetic fields will add linearly. (Vector fields adding to other vector fields)

This is the reason Biot-Savart's law works. You add (integrate) the induction of many small (infinitesimally so) elements of current together to get a total magnetic induction (and therefore field).

aiy1tm
Posts: 15
Joined: Thu Dec 06, 2007 8:03 am UTC

### Re: Magnets and Their Fields!

As others have already pointed out, magnetic fields do obey superimposition.

However, for a magnetised object placed into a uniform field, you either have to specify the magnetisation of the object (the tractable by hand case is uniformly magnetised sphere/long rod... this is the problem of a permanent magnet), or you have to specify the permeability of the object (ie: an object that has an induced magnet when it is exposed to magnetic fields, real world is always a little of both).

In either case, the problem can be distilled down to solving LaPlace's equation (for a quantity called the magnetic potential) for two regions with some boundary conditions. because the problem is free of source currents.

edit: working this out from scratch will probably just be equivalent to superimposing the result of a magnetised rod with a uniform field, but it is a nice check (and it is basically how you could figure out the field due to the rod if you didn't know it somehow already).